You're on the right track, but you just need some tweaks. I'm not going to write the code for you, but here are some clues.
If you want your function to return the index instead of the maximum value, then you need to change the way you compute the return value and the way you use it recursively.
private int getLargestElementLoca(int[] list, int count)
{
int largestValue;
if(count == 1){
return 0;
}
If there is only one element to look at, i.e. list[0], then list[0] will be the maximum, and 0 will be its index. So returning 0 is correct here.
int tempMax = getLargestElementLoca(list,count-1);
You've redefined getLargestElementLoca so that it returns an index, not a maximum value. That applies to your recursive call also, so tempMax is going to be an index and not a value. That means that you can't pass it directly into Math.max. Some adjustment will be necessary, but keep reading.
largestValue = Math.max(list[count-1],tempMax);
Math.max returns the largest value, but that isn't what you want. You have two indexes, count-1 and something else, and you want to compute the index of the larger value. You can't do that with Math.max, but you can use an if statement or the conditional operator a ? b : c. It would also be helpful to rename the variable, since it's no longer going to contain the largest value.